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In this article, distributed finite-time tracking control for nonlinear multi-agent systems subject to external disturbances is investigated. With the aid of sliding-mode control technique, both the finite-time consensus tracking in the presence of a single leader and the finite-time containment control with multiple leaders are in detail analysed. A distinctive feature of this work is that the communication topology among the followers can be directed. It is shown that the states of the followers can track that of the leader when there exists a single leader, and converge to a convex hull spanned by those of the leaders when there exist multiple leaders, both in finite time. Moreover, the finite convergence time is explicitly presented. Numerical examples are finally given to illustrate the theoretical results.

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SUMMARY This paper investigates the distributed finite‐time consensus‐tracking problem for coupled harmonic oscillators. The objective is to guarantee a team of followers modeled by harmonic oscillators to track a dynamic virtual leader in finite time. Only a subset of followers can access the information of the virtual leader, and the interactions between followers are assumed to be local. We consider two cases: (i) The followers can obtain the relative states between their neighbors and their own; and (ii) Only relative outputs between neighboring agents are available. In the former case, a distributed consensus protocol is adopted to achieve the finite‐time consensus tracking. In the latter case, we propose a novel observer‐based dynamic protocol to guarantee the consensus tracking in finite time. Simulation examples are finally presented to verify the theoretical analysis. Copyright © 2012 John Wiley & Sons, Ltd.